The following abbreviations that appear in the ensuing description are defined as follows:
MLMaximum LikelihoodMAPMaximum A PosterioriOFDMOrthogonal Frequency Division MultiplexingCIRChannel Impulse ResponseCPCyclic PrefixBERBit Error RateMSEMean Square ErrorPGAProgrammable Gate ArrayWLANWireless Local Area Network
A conventional channel estimation and synchronization approach performs each task sequentially based on a known preamble (training sequence) structure. For example, one known type of WLAN legacy preamble structure is designed such that initial frequency offset estimation is assumed to be operated on repetitive short preambles, while symbol timing estimation and channel estimation processes are expected to be based on a longer preamble.
There are other joint estimation approaches. One approach is to obtain joint symbol timing and channel estimation while assuming a carrier frequency offset being compensated (see Erik G. Larsson, Guoquing Liu, Jian Li, and Georgios B. Giannakis, “Joint Symbol Timing and Channel Estimation for OFDM Based WLANs”, IEEE Communication Letters, Vol. 5, No. 8, August 2001). Its joint estimation is based on the minimization of a known frequency domain preamble sequence where Akaike information criterion is used to jointly estimate the exact time offset and a channel length. Another approach is based on alternating projection algorithm (which solves multi-dimensional problems through an iterative one dimensional approach) to find the frequency offset estimation and thus obtain the channel estimation for an uplink OFDM system (see Man-On Pun, Shang-Ho Tsai, and C.-C. Jay Kuo, “Joint Maximum Likelihood Estimation of Carrier Frequency Offset and Channel in Uplink OFDMA Systems”, The IEEE 2004 Globecom PIMRC, Vol. 6, pp. 3748-3752 & Man-On Pun, C.-C. Jay Kuo and Michele Morelli, “Joint Synchronization and Channel Estimation in Uplink OFDMA Systems”, ICASSP 2005, pp. 857-860, referred to below as Pun et al). However, this approach assumes time synchronization of each user, and thus does not offer a full synchronization solution (both frequency offset and symbol offset estimation) and channel estimation simultaneously.
Recently, a closed form solution of joint synchronization and channel estimation has been proposed based on ML theory, but no ML parameter search methodology was provided (Wei Chee Lim, B. Kannan and T. T. Tjhung, “Joint Channel Estimation and OFDM Synchronization in Multipath Fading”, 2004 IEEE ICC Vol. 2, pp. 983-987, June 2004, referred to hereafter as Lim et al.).
In general, a conventional ML joint synchronization and channel estimation scheme faces computational complexity problems in regards to ML parameter search operations.